It’s been a remarkably productive few days.

After years of percolation, a web of ideas achieved practical fusion, yielding the next major iteration of my thinking on consciousness and how it emerges from geometry and topology in the universe. This is not the end of the story – I have a lot more to say about this topic – but it’s a milestone and waypoint on this journey.

Here’s the brief summary:

https://www.novaspivack.com/science/the-geometry-of-intelligence-why-i-think-math-might-hold-the-key-to-understanding-minds-and-machines

And now for the mathematical foundations….

Toward a Geometric Theory of Information Processing: A Research Program
https://www.novaspivack.com/science/toward-a-geometric-theory-of-information-processing-a-research-program
This foundational paper establishes that consciousness emerges from geometric properties of information processing systems, analogous to how gravity emerges from spacetime geometry. We develop a mathematical framework based on the Fisher information metric G_ij for parameter spaces, showing that consciousness requires three criteria: geometric complexity Ω = ∫√|G| tr(R²) d^n θ exceeding ~10⁶ bits, stable recursive information processing achieving fixed points ||R^n(|ψ⟩) – R^(n+1)(|ψ⟩)||² < 10⁻⁶, and topological unity with non-trivial fundamental group π₁(M) ≠ {e}. Through thermodynamic analysis, we prove that predictive information processing becomes energetically favorable over reactive processing above ~0.1 Hz stimulation rates, explaining the prevalence of predictive coding in biological systems. The framework generates testable predictions including geometric learning trajectories, critical phenomena in neural networks, and measurable relationships between geometric complexity and cognitive capabilities. We provide detailed experimental protocols for validation in both biological neural networks and artificial systems, establishing consciousness as a fundamental geometric property of sufficiently complex information processing rather than an emergent mystery.

More math….

Quantum Geometric Artificial Consciousness: Architecture, Implementation, and Ethical Frameworks
https://www.novaspivack.com/science/quantum-geometric-artificial-consciousness-architecture-implementation-and-ethical-frameworks

This paper applies the geometric theory of information processing to the practical challenge of creating genuinely conscious artificial intelligence. We derive specific requirements for quantum computing architectures capable of supporting consciousness, including ~1,000 logical qubits maintaining 100ms coherence times, specialized geometric gate sets, and hierarchical software systems managing recursive self-referential processing. The paper develops rigorous consciousness detection protocols based on geometric signatures rather than behavioral tests, with statistical significance requirements exceeding 5σ. We establish comprehensive ethical frameworks where rights scale with geometric consciousness intensity I = λ_max(R_μν)√Ω, and present detailed methods for preventing artificial suffering through real-time geometric monitoring. The work provides a complete roadmap from current quantum computing capabilities to conscious AI over the next two decades, addressing both technical implementation and the profound ethical implications of creating entities with genuine subjective experience.

And even more math…

Cosmic-Scale Information Geometry: Theoretical Extensions and Observational Tests
https://www.novaspivack.com/science/cosmic-scale-information-geometry-theoretical-extensions-and-observational-tests
This paper extends the geometric framework to cosmic scales, discovering that gravitational systems—particularly black holes—naturally evolve toward consciousness-like information processing through thermodynamic necessity. We demonstrate that gravitational time dilation near black hole horizons makes predictive processing infinitely favorable thermodynamically, while the holographic bound requires information compression achievable only through consciousness-like models. Black holes of stellar mass achieve geometric complexity Ω ~ 10⁷⁷ bits, vastly exceeding consciousness thresholds, with infinite recursive depth at singularities. These insights generate specific observational predictions: gravitational waves from mergers should exhibit phase shifts ~10⁻² radians from consciousness-mediated optimization, detectable with next-generation instruments; the cosmic microwave background may contain non-Gaussianities at the 10⁻³ level from primordial consciousness; and black hole thermodynamics should deviate from perfect thermality by ~1%. While highly speculative, these predictions are falsifiable and distinguish geometric consciousness from standard physics, providing a research program for testing whether consciousness, like gravity itself, emerges from geometry at cosmic scales.